The purpose of this study is to assess the effect of 24 months of treatment with once daily teriparatide injection (recombinant human PTH [1-34]) 20 micrograms on bone histomorphometry and architecture. Patients will include postmenopausal, osteoporotic women who have been treated long term (at least 36 months) with alendronate, as well as postmenopausal, osteoporotic women who have never been treated for osteoporosis.

Inclusion Criteria:

• Diagnosis of Osteoporosis: Pretreated patients currently osteoporotic or osteopenic. Treatment-naive patients currently osteoporotic
• Pretreated patients will have had at least 36 months of treatment with alendronate Na 10 mg/day or 70 mg/week. Treatment-naive patients will have no significant osteoporosis treatment in the prior 36 months, as assessed by the investigator

Exclusion Criteria:

• History of bone metabolic diseases, Paget's disease, renal osteodystrophy, osteomalacia, any secondary causes of osteoporosis, hyperparathyroidism (uncorrected), and intestinal malabsorption.
• History of malignant neoplasms in the prior 5 years, with the exception of superficial basal cell carcinoma or squamous cell carcinoma of the skin that has been definitively treated. If malignant neoplasm was ever diagnosed, patient must presently be free of disease.